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I looked all over for a date and got everything from "early 1800s" to "late 1800s" but nothing exact, so I had to make an educated guess. The first cameras practical enough to take such a photo were developed around 1840 and the excavations began in 1867.
It's true. Hitler wanted to move the Sphinx to his base on the other side of the moon. Of course, moving the whole thing would be too difficult, so they only took the nose.
Hah.
Just in case, though, I'll clarify: what I'd heard was that, when the German army was in Egypt in WWII, some German soldiers used the nose for target practice and pulverized it. No aliens required.
Edit: I'm remembering the story wrong: the target practice thing is attributed to Napoleon's troops using the nose as target practice for cannon. It'd unsubstantiated in either case; it turns out no one alive really knows.
Strangely the recent documentation doesn't mention that.
I hate to break it to you, but this information is heavily outdated.